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�9�cx��+?L�c�����6M���ٯ�N�p���}0[sm{�/0��{a�1�D|��[��� It is convenient to take the logarithm of the function first & then differentiate. 1 Burns, R (1971), Methods for individualizing instruction. 0 Implicit Differentiation Find y if e29 32xy xy y xsin 11 . Integration,unlike differentiation, is more of an art-form than a collection of algorithms. Consequently, students are failing because they cannot learn well with the methods through which they are being taught. In order to take derivatives, there are rules that will make the process simpler than having to use the definition of the derivative. different ways of learning, different interests, different ways of responding to instruction, and preferred ways of learning or expressing themselves (Ravitch 2007). A�ڂ��u��d������;'�ta��ccz~����nߵ���}}��;�]3�k����vٲpM[O�������+K��J��xw��?��,�16ql��{��=��x���n�vM�W������}�����)�����Ct��yIL�7�:Tu���r�^kW���:�]��u3�v��X�����KdeV�g�g�� Basic Short Cuts for Differentiation

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��J!��J���1�����.��cv��'߃g(;1K���d�� �k�!�P�Qw �1o� %PDF-1.7 Created: May 11, 2017| Updated: Oct 4, 2020, Calculus---Revision-Exercises-on-Methods-of-Differentiation. Differentiation requires the teacher to vary their approaches in order to accommodate various learning styles, ability levels and interests. 0000007833 00000 n able to come up with methods for approximating the derivatives at these points, and again, this will typically be done using only values that are defined on a lattice. �CqZ(�!F� �������̰�Fqy�*n�`����o�S�^�O�?9�t��&�-���� �۴v����J��c¡�.��}qL�J_�! 33 0 obj <> endobj 0000028357 00000 n �MFk����� t,:��.FW������8���c�1�L&���ӎ9�ƌa��X�:�� �r�bl1�

0000002056 00000 n trailer Exercise D involves logarithmic functions and Exercise E is on exponential functions. 4. �8���^����r���P�� 1 - Derivative of a constant function. H�\��j�0��~ xref Lecture by teacher (and what else can you do!) PART A: BASIC RULES OF DIFFERENTIATION In Section 3.2, we discussed Rules 1 through 4 below. 0000042539 00000 n >> 0000001156 00000 n �=-���4�F�_3��A� C#�9�Xb3B��2 Y��5�G�#,q�,qx1����+#q%/9q���R� ���S�%P!�H�!�8&��Q��h�\�tPr��(

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Many problems in applied mathematics involve the integration of functions given by complicated formulae, and practi-tioners consult a Table of Integrals in order to complete the integration. �'x?��.Pp�j�m��.Q�����3c Rememberyyx here, so products/quotients of x and y will use the product/quotient rule and derivatives of y will use the chain rule. Nm� �x�����J��=%^9�U'��9�4Z$��yc���5.� P� g���| �P�f@�70�U0¤�aR��9��nS8��i- ���� C/3;�&O�"&k&��L��Z]YYX�X�޲���p����30 ��@�X8�y�� � � endobj !Y��vك�z6s�������IH����@�Qx�x��k���00120�Ch�(9(���� 7�� endstream endobj startxref 0 %%EOF 753 0 obj <>stream The underlying function itself (which in this cased is the solution of the equation) is unknown. %PDF-1.6 %���� 2 • We have seen two applications: – signal smoothing – root finding • Today we look – differentation – integration • These will form the basis for solving ODEs SECTION 3.3: TECHNIQUES OF DIFFERENTIATION LEARNING OBJECTIVES • Learn how to differentiate using short cuts, including: the Linearity Properties, the Product Rule, the Quotient Rule, and (perhaps) the Reciprocal Rule. 5. 0000008647 00000 n That is, if c is a real number, then d dx!c"=0. ���8�H

Conditions. ?���:��0�FB�x$ !���i@ڐ���H���[EE1PL���⢖�V�6��QP��>�U�(j There are certain methods of x���wTS��Ͻ7�P����khRH �H�. Recitation oral questions by teacher answered orally by students (then what!) /Length 2596 0000022814 00000 n 0000009055 00000 n 2 0 obj 0000000016 00000 n Educational Technology, 11, p55-56 2 Zakhartchouck, J.M (2004), Au risque de la pédagogie différenciée, INRP. endstream endobj 41 0 obj[62 0 R] endobj 42 0 obj<>stream I�XPD(��58����%,�T(8"9ph%R`�R*2N�6І "�Ƃ$

150 Teaching Methods 1. 5fXL�5���P���*�RH'r�~*���u9�/g8�s���������$8�ԡF;sO�1�Ѣ�ט�h��&�C��z��J}�0��j��!������$S0tuL:l��e!n���'�g0�� /N 3 0000046496 00000 n %���� Differentiation techniques 151 chapter 4 Solution a To investigate the behaviour of f as x → −1, a table of values or a graph can be used. Wa�"����Q %PDF-1.4 %���� Later exercises are more advanced and differentiation may require a combination of methods. 75 0 obj<>stream

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A simple approximation of the first derivative is f0(x) ≈ f(x+h)−f(x) h, (5.1) The constant rule: The derivative of a constant function is 0. endstream endobj 43 0 obj<> endobj 44 0 obj<> endobj 45 0 obj<>stream

Numerical methods John D. Fenton a pair of modules, Goal Seek and Solver, which obviate the need for much programming and computations.

� I�C,�A�8��K����4,� �Z6�r� From below The table of values and associated graph above both suggest that as x → −1 from below, f(x) → 1. The questions (with separate answers) are contained in seven exercises. Techniques of Differentiation - Classwork Taking derivatives is a a process that is vital in calculus. startxref 0000004343 00000 n 5 acceptent que les garçons interrompent les filles, et s’adressent à eux avec des phrases courtes et directives. 124 questions for revision practice on methods of differentiation.

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Exercise F (trigonometric functions) and Exercise G (implicit functions) complete this package (a pdf on 15 A4 pages).

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�9�cx��+?L�c�����6M���ٯ�N�p���}0[sm{�/0��{a�1�D|��[��� It is convenient to take the logarithm of the function first & then differentiate. 1 Burns, R (1971), Methods for individualizing instruction. 0 Implicit Differentiation Find y if e29 32xy xy y xsin 11 . Integration,unlike differentiation, is more of an art-form than a collection of algorithms. Consequently, students are failing because they cannot learn well with the methods through which they are being taught. In order to take derivatives, there are rules that will make the process simpler than having to use the definition of the derivative. different ways of learning, different interests, different ways of responding to instruction, and preferred ways of learning or expressing themselves (Ravitch 2007). A�ڂ��u��d������;'�ta��ccz~����nߵ���}}��;�]3�k����vٲpM[O�������+K��J��xw��?��,�16ql��{��=��x���n�vM�W������}�����)�����Ct��yIL�7�:Tu���r�^kW���:�]��u3�v��X�����KdeV�g�g�� Basic Short Cuts for Differentiation

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0000002056 00000 n trailer Exercise D involves logarithmic functions and Exercise E is on exponential functions. 4. �8���^����r���P�� 1 - Derivative of a constant function. H�\��j�0��~ xref Lecture by teacher (and what else can you do!) PART A: BASIC RULES OF DIFFERENTIATION In Section 3.2, we discussed Rules 1 through 4 below. 0000042539 00000 n >> 0000001156 00000 n �=-���4�F�_3��A� C#�9�Xb3B��2 Y��5�G�#,q�,qx1����+#q%/9q���R� ���S�%P!�H�!�8&��Q��h�\�tPr��(

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Many problems in applied mathematics involve the integration of functions given by complicated formulae, and practi-tioners consult a Table of Integrals in order to complete the integration. �'x?��.Pp�j�m��.Q�����3c Rememberyyx here, so products/quotients of x and y will use the product/quotient rule and derivatives of y will use the chain rule. Nm� �x�����J��=%^9�U'��9�4Z$��yc���5.� P� g���| �P�f@�70�U0¤�aR��9��nS8��i- ���� C/3;�&O�"&k&��L��Z]YYX�X�޲���p����30 ��@�X8�y�� � � endobj !Y��vك�z6s�������IH����@�Qx�x��k���00120�Ch�(9(���� 7�� endstream endobj startxref 0 %%EOF 753 0 obj <>stream The underlying function itself (which in this cased is the solution of the equation) is unknown. %PDF-1.6 %���� 2 • We have seen two applications: – signal smoothing – root finding • Today we look – differentation – integration • These will form the basis for solving ODEs SECTION 3.3: TECHNIQUES OF DIFFERENTIATION LEARNING OBJECTIVES • Learn how to differentiate using short cuts, including: the Linearity Properties, the Product Rule, the Quotient Rule, and (perhaps) the Reciprocal Rule. 5. 0000008647 00000 n That is, if c is a real number, then d dx!c"=0. ���8�H

Conditions. ?���:��0�FB�x$ !���i@ڐ���H���[EE1PL���⢖�V�6��QP��>�U�(j There are certain methods of x���wTS��Ͻ7�P����khRH �H�. Recitation oral questions by teacher answered orally by students (then what!) /Length 2596 0000022814 00000 n 0000009055 00000 n 2 0 obj 0000000016 00000 n Educational Technology, 11, p55-56 2 Zakhartchouck, J.M (2004), Au risque de la pédagogie différenciée, INRP. endstream endobj 41 0 obj[62 0 R] endobj 42 0 obj<>stream I�XPD(��58����%,�T(8"9ph%R`�R*2N�6І "�Ƃ$

150 Teaching Methods 1. 5fXL�5���P���*�RH'r�~*���u9�/g8�s���������$8�ԡF;sO�1�Ѣ�ט�h��&�C��z��J}�0��j��!������$S0tuL:l��e!n���'�g0�� /N 3 0000046496 00000 n %���� Differentiation techniques 151 chapter 4 Solution a To investigate the behaviour of f as x → −1, a table of values or a graph can be used. Wa�"����Q %PDF-1.4 %���� Later exercises are more advanced and differentiation may require a combination of methods. 75 0 obj<>stream

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Mosaic Attenuation: Etiology, Methods of Differentiation, and Pitfalls 1

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Numerical methods John D. Fenton a pair of modules, Goal Seek and Solver, which obviate the need for much programming and computations.

� I�C,�A�8��K����4,� �Z6�r� From below The table of values and associated graph above both suggest that as x → −1 from below, f(x) → 1. The questions (with separate answers) are contained in seven exercises. Techniques of Differentiation - Classwork Taking derivatives is a a process that is vital in calculus. startxref 0000004343 00000 n 5 acceptent que les garçons interrompent les filles, et s’adressent à eux avec des phrases courtes et directives. 124 questions for revision practice on methods of differentiation.

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